Applying Dividend Discount Model (DDM) to 'State Bank of India' (SBI)

Dividend Discount Model values a firm's equity on the basis of the future dividends that the company is expected to give. Discounting all the future dividends gives the value of the stock as this is the only money an investor is going to get if he keeps the stock till perpetuity.

The general valuation formula for DDM is:
P = D1/(k - g)

where
P - ideal price of the stock
D1 - dividends for the year 1
k - cost of equity/ discounting rate
g - growth rate of the dividends

There are some assumptions in this model which require careful use of this model for finding the intrinsic value of a stock based on its dividends.

We will use a live example of State Bank of India (SBI) to illustrate the use of DDM. The following is the last 10 year dividend history of the company:

Year End	Total Dividends paid (Rs crores)	PAT (Rs crores)	Retained Earnings (Rs crores)	Retention ratio, b
Mar-98	211	1861	1650	0.89
Mar-99	211	1029	818	0.8
Mar-00	263	2051	1788	0.87
Mar-01	263	1880	1617	0.86
Mar-02	316	2423	2107	0.87
Mar-03	447	3105	2658	0.86
Mar-04	579	3681	3102	0.84
Mar-05	658	4305	3647	0.85
Mar-06	737	4405	3668	0.83
Mar-07	737	4534	3797	0.84

Using this we find that SBI has policy to retain about 85% of their earnings and distribute 15% as dividends to its shareholders. The retained earnings add on to the shareholder's equity and should earn profits for SBI. For each year we also looked into the returns on the equity (ROE) for SBI. the data is as follows:

Year End	Retention ratio, b	ROE	Growth rate, g
Mar-98	0.89	21.2	18.8
Mar-99	0.8	10.3	8.2
Mar-00	0.87	18.2	15.9
Mar-01	0.86	14.7	12.6
Mar-02	0.87	17	14.7
Mar-03	0.86	19.2	16.4
Mar-04	0.84	19.7	16.6
Mar-05	0.85	19.4	16.5
Mar-06	0.83	17	14.2
Mar-07	0.84	15.4	12.9

We have calculated the growth rate of dividends using:
growth rate = retention ratio X Return on equity ; g = b*ROE
Since dividends next year will be equal to this year's dividends plus the earnings on the retained earnings of this year with SBI.

The average growth rate for the 10 year period was about 14.7%.

SBI paid dividends of Rs 14 per share in 2007. Hence D0 = 14.
D1= 14*(1+g) = 14 * 1.147 ~ 16

Finding the discount rate is the trickiest part of the valuation and it depends on many factors and can be estimated using CAPM or other similar models. For simplifications we will take cost of equity as given in this case. We will take cost of equity as 15% and assume that SBI will enjoy this high growth for next 20 years before settling at something less than India's GDP growth rate (~ 7 %) and find out the value in the next article. Till then you can try it on your own.

[Hint: SBI is currently trading at 2400]


[To be completed in next post...]

Economic Fundae - GDP

Good Accounting turns data into information!

This article is aimed at people trying to understand the basics of national accounting.

GDP:Gross Domestic Product is the value of all the goods and services produced in the country within a given period. This includes all the goods and services produced in the geographical boundaries of the country irrespective of who produces. The other slight variant is the GNP which include receipts from abroad made as factor payments to domestically owned factor production. For example, part of India's GDP corresponds to the profits made by Hyundai Motors from its Indian operations. But these are part of the Korea's GNP because they are income of Korean-owned capital.

Although the difference is not significant in countries like U.S. it certainly is important where most of the countries labor is abroad working for a multinational company.

The fundamental national accounting equation will be as

Y= C + I + G + NX

Consumption spending by household sector, includes spending on anything under the sky. The only exception being the investment which people make in durable goods.

Then the government purchases are the government spending on the goods and services. Think of anything which government spends like laying roads, providing higher education etc. Again the only exception being the transfer payments. The transfer payments are those which does not get a service in return to government spending. This is logical as they are not a part of any of the current production.

The letter I in the equation refers to the Gross private domestic investment. In simple words, investment is associated with the business sector's adding to the physical stock of capital, which in turn will increase the economy's ability to produce output in the future.

The last term is the Net Exports, the difference between the exports and imports. They are to account for domestic spending on foreign goods and foreign spending on domestic goods. Confused, well we just finished the accounting of the entire nation. There is more than one reason to be confused, like most of our politicians.

Governments budget deficit is often a term we hear particularly in a country like India. This essentially means the difference between the government expenditures and the taxes received. Remember to include transfer payments as a part of government expenditures (which is slightly different from the government purchases)

Quick Fact:

GDP of India: (2007-08): 41,25,725 Crores of Rupees

Without further delay we will introduce you to other macroeconomic variables which are inflation, currency exchange rates, interest rates, monetary system and the business cycles.

Time Value of Money (Part 2)

Earlier we discussed about compounding by which we found out the future value of an amount deposited now.
Similar is the concept of discounting where we calculate the present value of a cash that is going to come in future.

PV - Present Value of an amount that will be received in the future, calculated after discounting. FV - Future Value of an amount invested now at a given rate of interest.

The rate used for compounding is the interest rate offered by the instrument in which the money is invested.
For discounting rate generally the cost of capital rate is used. This can be the rate which your money can grow with you.

Till now we had considered cash flow at one point of time and discussed ways to find its value at some other point of time. This kind of cash flow is known as lump-sum. What if the cash flow is divided and keeps on coming at different times. Four new terms are introduced for these:

Annuity - It is a regular cash flow for a fixed period of time.
Annuity Due- Cash flow occurs at the start of the period.
Annuity Ordinary- Cash flow occurs at the end of the period.
Perpetuity - It is a regular cash flow for a infinite period of time.

Generally, Annuity and Perpetuity are used for equal cash flows in each period.
If the cash flows are unequal it is called mixed stream.

The formula for future value of an ordinary annuity (FV) is:
where FVA(due) is future value of annuity due, A is equal cash flow per period for n periods compounded at interest rate r.
Similar formulae for present value are:
Present Value of a growing stream of cash flow:
Gordon Growth Model
g is growth rate of cash flow and if g < onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh7awFDFtnkqy-wTbUDBR2FLJDdcQDpfcIUeReymZnyAO7IqGLC2X9YeJaksDZ10WIrby-Y9zs9Rgzpeg7r-_1rQL8uTAoG2Jl1GS2CeQb6KHWTQuO3Uzu3lf-6ACKTsRaLejJAnCV8Ez0k/s1600-h/AnnuityGrow.jpg">
Change in Compounding interval

Time Value of Money

Like most of the things money also loses its value if kept idle. Its mainly because of inflation, which increases the cost of goods and the purchasing power of money decreases.

Its better to invest money in something which can give an interest which is more than inflation. Generally the safest place to keep your money is the banks. They give an interest on your deposit. Most of the time the interest is compounded. Compounding makes a big difference in the long run. Compounding essentially means that you will get interest on 'interest earned' besides the usual interest on the initial amount (principal). It keeps on accumulating period after period. Generally the interest rates are compounded annually - meaning the interest you will earn after the end of a year will start fetching you more interest from year end onwards.

Power of Compounding
Compounding creates a big difference in long run. The table shows the the Future Value of Rs 100 after several years.
One may ask that who has seen 200 years and from the table it appears that it doesn't make that big a difference during a short span, say of 10 years. But what happens if you get 20% interest rate.
Now certainly the difference cannot be neglected.
The formula used for calculating Future Value (FV) is pretty simple.

where FV is Future Value, PV is Present Value, r is rate of interest compounded periodically (generally compounded annually), n is the number of periods (eg. number of years if interest rate is compounded annually)
Next article we will discuss about Annuities.